refactor: extract psysonic-syncfs crate (M4/7)

Moves all on-disk cache + device-sync code out of the top crate:

  crates/psysonic-syncfs/                      new lib crate
    src/cache/{offline,hot,downloads,fs_utils} unchanged behaviour
    src/sync/{batch,device}                    (no tray.rs — that's UI)
    src/file_transfer.rs                       shared HTTP helpers
    src/lib.rs                                 + DownloadSemaphore type
                                               + sync_cancel_flags fn

The shell crate keeps `lib_commands/sync/tray.rs` (OS tray icon — UI
concern, will move to shell-tauri at M7) but drops the rest of
`lib_commands/cache/` and the syncfs sibling files.

Tauri command quirk surfaced and resolved: `#[tauri::command]` puts its
`__cmd__*` and `__tauri_command_name_*` helper macros at the *exact*
module of the function, and `pub use` doesn't carry them across module
boundaries. invoke_handler! in lib.rs now references each syncfs
command via its full deepest path
(`psysonic_syncfs::cache::offline::download_track_offline`, etc.) so
Tauri's macros resolve at the right scope. Same approach the audio
crate already uses (`audio::commands::audio_play`).

Cross-crate ref migrations applied via batch sed:
  crate::audio::*               → psysonic_audio::*
  crate::analysis_runtime::*    → psysonic_analysis::analysis_runtime::*
  crate::analysis_cache::*      → psysonic_analysis::analysis_cache::*
  crate::subsonic_wire_user_agent → psysonic_core::user_agent::*
  super::super::file_transfer:: → crate::file_transfer::

Behaviour preserving. Cargo check + clippy --workspace clean.

src-tauri/crates/psysonic-syncfs/src/cache/fs_utils.rs

@@ -0,0 +1,53 @@
+use std::path::Path;
+
+/// Recursively sums the size of all files under `root`.
+/// Missing roots, unreadable directories, and unreadable files are silently skipped.
+pub fn dir_size_recursive(root: &Path) -> u64 {
+    if !root.exists() {
+        return 0;
+    }
+    let mut total: u64 = 0;
+    let mut stack = vec![root.to_path_buf()];
+    while let Some(dir) = stack.pop() {
+        let rd = match std::fs::read_dir(&dir) {
+            Ok(r) => r,
+            Err(_) => continue,
+        };
+        for entry in rd.flatten() {
+            let path = entry.path();
+            if path.is_dir() {
+                stack.push(path);
+            } else if let Ok(meta) = std::fs::metadata(&path) {
+                total += meta.len();
+            }
+        }
+    }
+    total
+}
+
+/// Walks upward from `start_dir`, removing each empty directory using `remove_dir`
+/// (never `remove_dir_all`). Stops as soon as a non-empty directory is hit, the
+/// boundary is reached, or removal fails.
+///
+/// `boundary` is never removed and is treated as a hard stop. If `start_dir` is
+/// not under `boundary`, the function is a no-op.
+pub fn prune_empty_dirs_up_to(start_dir: &Path, boundary: &Path) {
+    let mut current = Some(start_dir.to_path_buf());
+    while let Some(dir) = current {
+        if dir == boundary || !dir.starts_with(boundary) {
+            break;
+        }
+        match std::fs::read_dir(&dir) {
+            Ok(mut entries) => {
+                if entries.next().is_some() {
+                    break;
+                }
+                if std::fs::remove_dir(&dir).is_err() {
+                    break;
+                }
+                current = dir.parent().map(|p| p.to_path_buf());
+            }
+            Err(_) => break,
+        }
+    }
+}